A novel circular dynamics in financial networks with cross-correlated volatility and asset movements

In this paper, we propose a novel application of classical directional statistics to model the cross-correlation of asset volatility in financial networks. The proposed novel Circular Volatility Model (CVM) provides a framework for studying the interdependencies of financial assets whose returns exhibit periodic behaviors. By extending traditional volatility models into a circular framework, we establish new pathways for understanding the cyclicity inherent in market dynamics. Our model is rigorously grounded in classical \& directional statistics, utilizing von Mises distributions for parameter estimation and novel circular covariance structures. We offer formal derivations, maximum likelihood estimates, and a novel goodness-of-fit testing framework for this circular model. We establish our methodologies using simulation studies.